A Review of Some Modern Approaches to the Problem of Trend Extraction

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Comparison of methods for non-stationary hydrologic frequency analysis: Case study using annual maximum daily precipitation in Taiwan (2017, methodology): “…of climatic conditions has not been limited to theoretical or modeling studies but also from data observation; evidence of an increasing trend in flood peaks has also been identified in the time series of floods using statistical methods (Burn, 1998; Steel, 1998; Aliev and Vishnevskyi, 1998).”
Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature (2012, background): “For example, in economics the annual cycle is usually referred to as a trend (Alexandrov et al. 2008).”
Trend Filtering Methods for Momentum Strategies (2011, background): “In this case, the trend-cycle model becomes:  y (1) t .”